A text message is sent to five friends. Each of the five friends then forwards it to five other friends and

Question

each of these people also sends it to five other friends. How many people does the text message reach,
not including those who forwarded the message?

Answer 1

To determine how many people the text message reaches without counting those who forwarded it, let's break it down step by step.

1. Initial message: The message is sent to 5 friends.

   • So, at this point, we have 5 people who receive the message directly.

2. First round of forwarding: Each of the 5 friends forwards the message to 5 additional friends.

   • Each of the 5 friends forwards it to 5 people: \( 5 \times 5 = 25 \) new recipients.

3. Second round of forwarding: Each of the 25 new friends also forwards the message to 5 more friends.

   • Each of these 25 people forwards it to 5 people: \( 25 \times 5 = 125 \) new recipients.

Now we have a total reach which is the sum of all distinct recipients across these stages.

• Recipients from the initial text: 5
• Recipients from the first forwarding round: 25
• Recipients from the second forwarding round: 125

Now, we can calculate the total number of people reached:

\[ 5 + 25 + 125 = 155 \]

Thus, the total number of people that the text message reaches, not including those who forwarded it, is \( \boxed{155} \).